Material models of dark energy

Abstract

We review and develop a new class of "dark energy" models, in which the relativistic theory of solids is used to construct material models of dark energy. These are models which include the effects of a continuous medium with well defined physical properties at the level of linearized perturbations. The formalism is constructed for a medium with arbitrary symmetry, and then specialised to isotropic media (which will be the case of interest for the majority of cosmological applications). We develop the theory of relativistic isotropic viscoelastic media whilst keeping in mind that we ultimately want to observationally constrain the allowed properties of the material model. We do this by obtaining the viscoelastic equations of state for perturbations (the entropy and anisotropic stress), as well as identifying the consistent corner of the theory which has constant equation of state parameterẇ = 0. We also connect to the non-relativistic theory of solids, by identifying the two quadratic invariants that are needed to construct the energy-momentum tensor, namely the Rayleigh dissipation function and Lagrangian for perturbations. Finally, we develop the notion that the viscoelastic behavior of the medium can be thought of as a non-minimally coupled massive gravity theory. This also provides a tool-kit for constructing consistent generalizations of coupled dark energy theories. Contents

Gravitational wave constraints on dark sector models

“…For completeness we have also included the entropy perturbation Γ m and the anisotropic stress Π S m for the matter component which are typically negligible in the regime relevant to observations of cosmic acceleration; in the subsequent discussions we will ignore these terms. The coefficients (C ij ) have been computed for k-essence [68][69][70], kinetic gravity braiding [19], f (R) [67], Horndeski theories [45], generalised Einstein-Aether [61], elastic dark energy [65,66] and Lorentz-violating massive gravity models [71]. In full generality they are free functions of the scale factor (and hence cosmic time) and scale via the wave number, usually entering as a k 2 term due to the presumed dependence on second order combinations of spatial derivatives.…”

f(R)gravity as a dark energy fluid

“…where the list of arguments shown is not exhaustive and can include derivatives, for example. Certain classes of equation of state have already been worked out (see [12,13] for kinetic gravity braiding models, [27] for coupled Horndeski theories, [28] for generalised scalar-tensor theories and [29][30][31] for relativistic elastic and viscoelastic material models).…”

Effective field theory of broken spatial diffeomorphisms

“…Several other gravitational phenomena associated with broken spatial diffeomorphisms have also been discussed in the literature [48][49][50][51][52][53][54][55][56], without relating them explicitly to the massive gravity aspect of the theory. For example, by tuning the form of higher order interactions, ref.…”